AUSTIN, Texas (Reuters) - Texas Attorney General Greg Abbott on Tuesday asked a federal appeals court judge to immediately reinstate a restriction on abortion that a lower court judge had ruled unconstitutional, according to a court filing.

A federal district court judge on Monday ruled unconstitutional a provision requiring physicians who perform abortions to have an agreement with a local hospital to admit patients. That was part of a sweeping new Texas law restricting abortions that was set to go into effect on Tuesday.

Abbott, a Republican who is running for Texas governor, asked the 5th Circuit Court of Appeals to overturn that ruling by the end of the day, and requested a full court hearing on the issue in January.

The Texas law passed in July was the most fiercely debated proposal to restrict abortions in the United States this year. Republican efforts to pass the law sparked an unsuccessful filibuster by Democratic state Senator Wendy Davis, which propelled her into the national spotlight and encouraged her to announce she will run for governor.

The contest between Abbott and Davis is expected to be one of the top gubernatorial races in the nation next year.

The Monday ruling by U.S. District Judge Lee Yeakel came in response to a lawsuit by abortion-rights supporters including the American Civil Liberties Union, Planned Parenthood, and Texas clinics.

The groups said the law would force the closure of more than a dozen clinics statewide and cut off access to health services for some 22,000 women. Yeakel agreed that the new restriction would make it harder for women seeking a legal abortion.

Abbott argued in his court filing Tuesday that there was no proof yet that any of that would happen - and that it could not be proven until after the law went into effect.

In their response to the appeals court on Tuesday, Planned Parenthood and the groups which had challenged the law said there was no need to immediately reinstate the provision the state of Texas would not be harmed if the matter were resolved using the normal appeals process.

The U.S. Fifth Circuit Court of Appeals has shown a willingness to allow abortion restrictions. In 2012, it allowed a law requiring women seeking an abortion to undergo a transvaginal ultrasound to go into effect, reversing a halt imposed by a lower court.

Parts of the Texas law went into effect on Tuesday, including a provision that bans abortions beyond 20 weeks gestation which was not contested by Planned Parenthood and other clinics.